Are neutrinos particles? If so, are they material particles that travel through other matter?

Yes, neutrinos are particles and they have mass even though their mass is extremely tiny. A typical electron-neutrino mass is measured at about 1.85 eV or lower, which is equal to about 6.697 x 10^-37 Kg. In comparison, the rest mass of an electron is 511,000 eV (0.511 MeV) which is equal to ~ 9.109 x 10^-31 Kg, 6 orders of magnitude lower.
Neutrinos tend to pass through other matter with an extremely low probability of interacting. This is because they do not have the ability to interact electromagnetically or through the strong or color force.
Aside from gravitational attraction (which is hard to detect at low mass), neutrinos only interact through the weak nuclear force, which means they have an infinitesimally small probability of interacting and generally only with quarks in the nuclei of atoms which are also tiny and unlikely for the neutrino to hit.
Right this moment, about 65 billion neutrinos streaming from the Sun have passed through every square centimeter of your body and will continue through the Earth with very few hitting another piece of matter. This makes detecting neutrinos difficult and requires large pools of water, or chlorine, or gallium surrounded by photon detectors all buried in a deep mine (so they won’t be triggered by cosmic rays). When a neutrino interacts with a quark, it can change its flavor (ie. up to down quark) changing the element (ie. gallium to germanium, oxygen to fluorine) and releasing a photon of specific energy that can be picked up by the detectors.
Here is a picture of the inside of the Borexino neutrino detector tank deep underground in Italy.
                                                    
Since the vast majority of neutrinos pass through matter, detectors can be used to make images of the core of the Sun where they are created by fusion reactions. Here is an picture of the fusing areas of the solar core, imaged by neutrinos.
  

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